Est.Ratio {samplingVarEst} | R Documentation |
Estimator of a ratio
Description
Estimates a population ratio of two totals/means.
Usage
Est.Ratio(VecY.s, VecX.s, VecPk.s)
Arguments
VecY.s |
vector of the numerator variable of interest; its length is equal to |
VecX.s |
vector of the denominator variable of interest; its length is equal to |
VecPk.s |
vector of the first-order inclusion probabilities; its length is equal to |
Details
For the population ratio of two totals/means of the variables y
and x
:
R = \frac{\sum_{k\in U} y_k/N}{\sum_{k\in U} x_k/N} = \frac{\sum_{k\in U} y_k}{\sum_{k\in U} x_k}
the ratio estimator of R
(implemented by the current function) is given by:
\hat{R} = \frac{\sum_{k\in s} w_k y_k}{\sum_{k\in s} w_k x_k}
where w_k=1/\pi_k
and \pi_k
denotes the inclusion probability of the k
-th element in the sample s
.
Value
The function returns a value for the ratio point estimator.
Author(s)
Emilio Lopez Escobar.
References
Hajek, J. (1971) Comment on An essay on the logical foundations of survey sampling by Basu, D. in Foundations of Statistical Inference (Godambe, V.P. and Sprott, D.A. eds.), p. 236. Holt, Rinehart and Winston.
Horvitz, D. G. and Thompson, D. J. (1952) A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47, 663–685.
Narain, R. D. (1951) On sampling without replacement with varying probabilities. Journal of the Indian Society of Agricultural Statistics, 3, 169–175.
See Also
VE.Jk.Tukey.Ratio
VE.Jk.CBS.HT.Ratio
VE.Jk.CBS.SYG.Ratio
VE.Jk.B.Ratio
VE.Jk.EB.SW2.Ratio
Examples
data(oaxaca) #Loads the Oaxaca municipalities dataset
pik.U <- Pk.PropNorm.U(373, oaxaca$HOMES00) #Reconstructs the 1st order incl. probs.
s <- oaxaca$sHOMES00 #Defines the sample to be used
y1 <- oaxaca$POP10 #Defines the numerator variable y1
y2 <- oaxaca$POPMAL10 #Defines the numerator variable y2
x <- oaxaca$HOMES10 #Defines the denominator variable x
Est.Ratio(y1[s==1], x[s==1], pik.U[s==1]) #Ratio estimator for y1 and x
Est.Ratio(y2[s==1], x[s==1], pik.U[s==1]) #Ratio estimator for y2 and x